Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations
1
Facultad de Ciencias Actuariales, Universidad Anáhuac México, Huixquilucan, Edo. de México 52786, Mexico
2
Department of Applied Mathematics, St. Petersburg State University, Saint Petersburg 198504, Russia
3
Bwin Interactive Entertainment AG, 1030 Vienna, Austria
*
Author to whom correspondence should be addressed.
†
Current address: Av. Universidad Anáhuac, No. 46 Col. Lomas Anáhuac, Huixquilucan, Edo. de México 52786, Mexico.
‡
These authors contributed equally to this work.
Mathematics 2020, 8(7), 1081; https://doi.org/10.3390/math8071081
Received: 25 May 2020 / Revised: 25 June 2020 / Accepted: 29 June 2020 / Published: 3 July 2020
(This article belongs to the Special Issue Game Theory)
This work presents a two-player extraction game where the random terminal times follow (different) heavy-tailed distributions which are not necessarily compactly supported. Besides, we delve into the implications of working with logarithmic utility/terminal payoff functions. To this end, we use standard actuarial results and notation, and state a connection between the so-called actuarial equivalence principle, and the feedback controllers found by means of the Dynamic Programming technique. Our conclusions include a conjecture on the form of the optimal premia for insuring the extraction tasks; and a comparison for the intensities of the extraction for each player under different phases of the lifetimes of their respective machineries.
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Keywords:
differential games; random time horizon; time until failure; discounted equilibrium; weibull distribution; chen distribution; equivalence principle
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MDPI and ACS Style
López-Barrientos, J.D.; Gromova, E.V.; Miroshnichenko, E.S. Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations. Mathematics 2020, 8, 1081. https://doi.org/10.3390/math8071081
AMA Style
López-Barrientos JD, Gromova EV, Miroshnichenko ES. Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations. Mathematics. 2020; 8(7):1081. https://doi.org/10.3390/math8071081
Chicago/Turabian StyleLópez-Barrientos, José D.; Gromova, Ekaterina V.; Miroshnichenko, Ekaterina S. 2020. "Resource Exploitation in a Stochastic Horizon under Two Parametric Interpretations" Mathematics 8, no. 7: 1081. https://doi.org/10.3390/math8071081
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